Are you open to a new project? or Are you open for a new project?

Question

These two statements seem correct, but actually, which one is the proper statement? And can you explain how the usage of to & for changes the meaning of the statement?

Hey, are you open to a new project?

or

Hey, Are you open for a new project?

Answer 1

1

Hey, are you open to a new project?

2

Hey, are you open for a new project?

In this context, we should use your example (1), with open to.

open to means willing to consider as shown in Cambridge Dictionary, definition C1 for open.

I'd like to think I'm open to (= willing to consider) any reasonable suggestion.

for is found in an example under another definition for open, meaning not decided.

We can leave our offer open for another week, but we have to have your decision by then.

This definition is not applicable to your example.

Edit: open for is an idiom, which means

to perform before (the main performer at a concert, show, etc.)

That definition is also not applicable to your example.